In the transmission of a television signal containing a luminance signal between a transmitting station and a receiving station of a television system, the picture resolution at the receiving station is compatibly increased by: effecting planar prefiltering of the luminance signal at the transmitting station and a corresponding planar postfiltering of the luminance signal at the receiving station; effecting offset sampling or offset modulation of the luminance signal at the transmitting station and a corresponding sampling conversion or demodulation of the luminance signal at the receiving station; deriving an additional signal from the luminance signal for increasing picture resolution, reducing the amplitude of the additional signal at the transmitting station and transmitting the additional signal together with the original luminance signal to the receiving station; and increasing the amplitude of the additional signal at the receiving station to an extent corresponding to the reduction performed at the transmitting station.